Short form of Elizabeth, not used before the 19th century, when it became popular in America and elsewhere after publication of Louisa M. Alcott's novel Little Women (1868), in which Beth March is one of the four sisters who are the central characters.
German: 1. (mainly Switzerland) from a derivative of Butzo, a pet form of the personal name Burkhard (see Burkhart). 2. (Bütz(e)): topographic name for someone who lived near a well, from Middle High German bütze ‘well’, ‘puddle’ (from Latin puteus). 3. South German: nickname from Middle High German butze denoting something small: an apple core, a small piece of something left over, a small person, a poltergeist.